超薄涂层结构断裂行为和失效分析的快速边界元法研究

Ultra-thin layered coatings can be used as barrier structures to improve the adhesion, diffusion, heat conduction and wear performances of many engineering devices and components. Having a clear understanding about the facture damage behavior of thin-layered coating systems is very useful and important. However, the rather complex and expensive experimental investigations on cracked ultra-thin films and coatings underlie a general lack of the analytical or numerical modeling efforts which can accurately and efficiently predict the performances of ultra-thin layered coating structures. The difficulties associated with such an analysis will be overcome in this project by using an advanced boundary element method (BEM). The scientific problems to be addressed include: (1) develop a new regularization technique for the accurate evaluation of nearly singular boundary element integrals, which are crucial in the applications of the BEM to thin shapes. Particular focus is on integrals with near strong-singularities and beyond; (2) establish new crack propagation simulation models for cracked thin-walled structures; (3) develop new fast multipole BEM formulations for modeling large-scale problems that can contain tens of thousands of cracks. Advanced boundary integral equations for thin-bodies, new preconditioners based on cracks, parallel computing and other techniques will be employed to tackle the challenges in the project. The research achievements of this project will serve as powerful analysis and modelling tools for fatigue invalidation analysis and structural optimization design of thin-layered coating systems.

表面涂层材料以优异的耐高温、耐磨损、耐腐蚀等性能，在现代机械加工和国防尖端技术领域得到了广泛的应用。现代工程中的涂层厚度一般在微米甚至纳米级，受涂层厚度和表面特征长度超大尺寸比的影响，涂层结构裂纹扩展和失效分析的精确数值模拟长期以来是一个挑战性的难点课题。本项目拟发展一种能有效分析超薄涂层结构断裂力学分析的三维快速边界元法计算模型，探索不同荷载形式、不同涂层厚度和不同材料组合等因素对涂层结构断裂力学行为和失效机理的影响。重点研究边界元法在模拟薄体结构问题时遇到的各类近奇异积分(特别是高阶近奇异积分)的通用正则化算法，建立适合于薄体结构边界元分析的裂纹扩展计算模型，探索适用于大规模裂纹扩展分析的快速多极边界元求解策略，充分发挥边界元法在薄体结构和动态裂纹扩展问题中的传统优势，为涂层结构的优化设计、失效分析和寿命预测等提供新的高效数值模拟手段。

表面涂层材料以优异的耐高温、耐磨损、耐腐蚀等性能，在现代机械加工和国防尖端技术领域得到了广泛的应用，其理论与应用也是固体力学领域中经典而又富有活力的研究领域之一。然而，涂层材料的相对厚度(狭长比)一般在微米甚至纳米级，受其厚度尺寸的影响，涂层材料中裂纹扩展的数值模拟一直是工程中的难点。尽管近几十年来超薄涂层材料的数值算法研究取得了快速的发展，有限元、有限差分等传统数值方法在模拟超薄涂层材料时仍面临复杂域网格剖分困难、计算量大和非对称稠密矩阵计算等挑战性难点问题。特别是涂层材料的狭长比小到纳米级时，传统方法的有效性受到了很大的限制。本项目发展了一种能有效分析超薄涂层结构断裂力学分析的快速边界元法计算模型，研究了不同荷载形式、不同涂层厚度和不同材料组合等因素对涂层结构断裂力学行为和失效机理的影响。主要研究成果包括：(1)针对边界元法在模拟薄体结构问题时遇到的各类近奇异积分(特别是高阶近奇异积分)的计算难题，发展了适用于超薄涂层结构断裂力学分析的近奇异积分新型正则化算法；(2)建立了一种能精确表征复合材料界面裂纹振荡特性的“特殊裂尖单元法”及其相应的奇异积分处理技术，通过裂尖单元的张开位移或界面应力实现复应力强度因子和能量释放率的直接求解；(3)探索适用于大规模裂纹扩展分析的快速多极边界元求解策略，充分发挥边界元法在薄体结构和动态裂纹扩展问题中的传统优势。本项目的研究成果为涂层结构的优化设计、失效分析和寿命预测等提供新的高效数值模拟手段。